Chapter 10, Problem 21RE

To determine

To find: The graph of the equation without applying the rotation of axis.

Answer to Problem 21RE

Parabola.

Explanation of Solution

Given:

$9x²-12xy+4y²+8x+12y=0$

Formula Used:

The Equation $Ax²+Cy² +Dx+Ey+F=0, B\ne 0$.

a. Defines a parabola if $B²-4AC=0$.

b. Defines an ellipse (or Circle) if $B²-4AC<0$.

c. Defines a hyperbola if $B²-4AC>0$.

Calculation:

Consider the given equation $9x²-12xy+4y²+8x+12y=0$.

$A=1 \text{and} B=-12\text{ and }C\text{ = 4}$.

$B^2-4AC=144-4\ast 9\ast 4=0$

Therefore, the equation defines a parabola.